In Minecraft Vanilla, you can get up to 7,558,272 items in a single double chest.
This using the technique of packing up tons upon tons of gold nuggets.
1 Double Chest = 54 slots.
1 Shulker Box = 27 slots.
Each slot could contain up to 64 items.
First we get 64 gold nuggets, then 64*9 = 64 gold ingots (Which would be 576 gold nuggets)
Then 576*9 = 5,184 (Which would be 64 gold blocks or 576 gold ingots or 5,184 gold nuggets)
Then, we fill up a shulker box with gold blocks, which would be 5,184*27 = 139,968 (Which would be 1,728 gold blocks or 15,552 gold ingots or 139,968 gold nuggets)
Then we fill up a double chest with shulker boxes already filled up with gold blocks, that would be:
139,968*54 = 7,558,272 (Which would be 93,312 gold blocks or 839,808 gold ingots or 7,558,272 gold nuggets)
That is actually possible in Vanilla Minecraft. I could go ever farther using golden apples, but I didn't because all this math means that you could actually turn everything back to gold nuggets If you wanted to.

Mind blown on the Ctrl+pick block grabbing nbt data, I’ve been playing MC for 7+ years and could never figure out how to do that! How do you make it place stacks of items like that into the chest though?